A Test of CPT and Lorentz Invariance from Muonium Spectroscopy

Upon a suggestion of Kostelecky et al., we have performed a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. New terms in their standard model extension violating CPT and Lorentz symmetry would appear as anti-correlated frequency shifts, oscillating at the earth's sidereal frequency, in the two ground state hyperfine transitions involving muon spin flip, $\nu_{12}$ and $\nu_{34}$, which were measured in a strong magnetic field of 1.7 T. No such time dependence was observed in $\nu_{12}$ or $\nu_{34}$ at the level of 20 Hz, limiting the size of some CPT and Lorentz violating parameters with Planck scale sensitivity, and representing almost an order of magnitude improvement over previous limits for the muon.